Lyapunov Exponents are asymptotic quantities that describe properties of chaotic attractors. Their computation is subject to various error sources stemming from the nonlinear system, the linearized system and from limiting the integration time. In this talk, I will describe the effects of these error sources and discuss how to analyze them. First results are obtained for errors stemming from the linearized system, which can be tackled by stepsize variations, whereas nonlinear effects are still an open problem. Our current approach intends to analyze nonlinear effects through spectral properties of the Koopman semigroup.